【摘要】 贝叶斯方法现已成为一种新的科学范式，尤其体现于当前迅速发展的人工智能领域，它为AI系统提供了处理不确定性和动态更新概率的推理框架。从基本原理上讲，贝叶斯定理为人们从验前概率过渡到验后概率提供了逻辑依据，成为人们根据经验证据来改变置信度的理性指导。然而，贝叶斯定理本身的合理性何在？这是休谟的归纳问题在贝叶斯方法中的体现，具体呈现为贝叶斯条件化规则的合理性问题。对此可提出“最小初始概率原则”给以回答。贝叶斯方法在科学推理的应用上，一个显著方面是用多理论检验模型取代传统的单理论检验模型即假设—演绎法，这不仅符合科学史的实际案例，而且通过“意见收敛定理”得到理论上的辩护。意见收敛定理的前提条件是可交换性，对之加以分析和澄清，可使该定理的应用范围从简单的重复独立试验扩展到复杂的科学验证。更多还原

【Abstract】 Bayesian method have emerged as a new scientific paradigm, particularly significant in the fast-growing field of artificial intelligence. It provides an inference framework for AI systems to handle uncertainties and dynamically update probabilities. Fundamentally, Bayes’ theorem establishes the logical basis for transitioning from prior probabilities to posterior probabilities, and becomes a rational guidance for people to change their degree of belief according to empirical evidence. However, the rationality of Bayes’ theorem itself remains a question—this reflects Hume’s problem of induction in Bayesian methodology. Specifically, it is manifested as the question of justifying for the principle of Bayesian conditionalisation. To address this, we propose the “principle of minimum initial probability”. A notable application of Bayesian method in scientific inference involves replacing traditional single-theory testing models(i.e., hypothetico-deductive method) with multi-theory testing model. This approach not only aligns with the cases in scientific history but also receives the theoretical justification through the convergence theorem for opinions. We analyze and clarify the concept “exchangeability” that is the prerequisite of the convergence theorem for opinions, thereby expanding its applicability from simple repeated independent trials to complex scientific processes of confirmation.更多还原